66
Convenient ways to calculate
Textbook: Part 2, lesson 66, pp. 84–86
GoalPerimeter of polygons, compound lengths and inverse operations.
New words
polygon · ko‘pburchakperimeter · perimetrinverse operation · teskari amalunknown · noma’lum
Explanation
The perimeter of a polygon is the sum of all its sides. The perimeter of a rectangle with corners cut off (a staircase shape) equals the perimeter of the rectangle itself: P = a + b + a + b. When adding compound lengths we add m, dm and cm separately. We find an unknown number with the inverse operation: if x + 365 = 5 120, then x = 5 120 − 365 = 4 755.
Worked examples
A shape cut from a 60 m × 30 m rectangle at the corners: P = 2 × (60 + 30) = 180 m.
2 m 6 dm 5 cm + 1 m 7 dm 8 cm = 3 m 13 dm 13 cm = 4 m 4 dm 3 cm.
Class activity
“Staircase”: draw a rectangle on squared paper, cut corner squares off (with an adult’s help for scissors) and compare the perimeter with the rectangle’s.
Practice
1
Corners were cut from a 30 m by 60 m rectangle to make a staircase shape. What is its perimeter in m?
180
2
x + 365 = 5 120. Find x.
4755
3
x : 24 = 37. Find x.
888
4
Find 2 m 6 dm 5 cm + 1 m 7 dm 8 cm.
4 m 4 dm 3 cm